Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C41 · Schur multiplier (H2) = C25 |
| direct product | C41×#3407 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C41 | C24 |
| commutator | C2 | C23×C8×C41 |
| Frattini, cosocle | C8 | C24×C41 |
| socle | C2×C41 | C23×C8 |
| prime radical | C2×#41×C41 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C41 ◁ G | |
360 conjugacy classes of subgroups.
2788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#12618, C41×#12833, C41×#12915, … |
| maximal normal subgroup of | C41×#12618, C41×#12833, C41×#12915, … |
| maximal quotient of | C41×#33324, C41×#33326, C41×#33333, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2139);